During phase I the Maximum Tolerated Dose (MTD) of belinostat in combination with carboplatin and paclitaxel will be determined in patients with Stage IV non-small cell lung cancer who have received no prior systemic chemotherapy. The dose escalation study will be conducted using traditional escalation rule of 3+3 design, during the first cycle of therapy. Belinostat will be assessed at a starting dose level of 1000 mg/m2 and multiple dose levels may be evaluated. Doses of belinostat, carboplatin and paclitaxel will remain constant throughout the study, unless dose modification is required by toxicity. Treatment is given on days 1-5 of every 21-day cycle. Routine safety evaluations will be conducted on days, 1, 8, and 15 of every cycle. Tumor measurement will be done after every 2 cycles of the treatment.